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Determining secant slope and tangent slope. Slope is the rate of change or Secant slope the slope between two points tangent slope the slope at one point of contact and is based upon a limit. Noun: derivative Verb: differentiation or to differentiate. If from a graph, use

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Application example of Tangent vs. Secant slope Height m age years Secant line, “smoothes out the curve between two points and assumes an average rate of growth over that time interval Tangent slope, at an instance type data based upon the limiting values of height just to the “immediate” left and just to the “immediate” right of the one contact point. This tangent slope position and value indicates the individual was having a growth spurt.

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Secant slope through (4, -2) and (6,2) Rise= 2-(-2) or 4 Run = 6-4 or 2 Tangent slope of line drawn at the one contact point of (0,2) Rise= - 6 Run = 2 Estimated from the “hand-drawn” tangent line Now use the PQ chart method to determine this tangent slope. Secant slope

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Find an equation of the tangent line to the curve at the point (2, 1).

Find an equation of the tangent line to the curve at the point (2, 1).

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